Pokémon: The First Movie, also known as Pocket Monsters: Mewtwo Strikes Back! (劇場版ポケットモンスター ミュウツーの逆襲 Gekijoban Poketto Monsuta Myutsu no Gyakushu), is the first theatrical release based on the Pokémon anime. Like the anime, it is directed by Kunihiko Yuyama.

The title Mewtwo Strikes Back is a direct translation of the movie’s Japanese name, Mewtwo no gyakushu, which can also be interpreted as Mewtwo’s Counterattack. The former title can be seen as a reference to Star Wars Episode V: The Empire Strikes Back, while the latter can be seen as a reference to Mobile Suit Gundam: Char's Counterattack.

As Pokémon was extremely popular back when this movie came out, it was a box office hit worldwide. It primarily consists of three segments: “Pikachu’s Vacation”, a 20+ minute feature focusing on the most popular Pokémon character Pikachu; "Origin of Mewtwo", a 10-minute featurette that functions as a prologue to the main feature; and Mewtwo Strikes Back, the main 76-minute movie feature. However, the United States dub omitted "Origin of Mewtwo" from the package before its U.S. theatrical run due to its dark nature, as the target MPAA rating was a G; it was partially restored in the movie's release on VHS and DVD. The featurette was eventually dubbed and restored as a special feature in the U.S. release of the direct-to-video movie sequel Pokémon: Mewtwo Returns.

The premiere criminal organization in the Pokemon world, Team Rocket, led by the devious Giovanni, desires a Pokémon stronger than any other that can be used as a military weapon for world conquest, so Giovanni funds the creation of a genetically enhanced "super-clone" of the extremely rare, powerful Pokémon Mew. The project , codenamed Mewtwo, goes awry as the being awakens and destroys the lab after discovering his clone nature. Giovanni arrives, intent on presenting himself as a different type of human which Mewtwo can trust so that he can control the errant Pokémon, and Giovanni offers to help add value to Mewtwo's life. Mewtwo agrees, believing that he will find his true purpose through Giovanni's aid.

Over the next few weeks, Giovanni assigns Mewtwo to a wide array of criminal Team Rocket operations involving the capturing of Wild Pokémon, among other things. Eventually, however, Mewtwo learns the truth from Giovanni about his existence—that he was created as an unquestioning war weapon for Team Rocket—and therefore embitters Mewtwo's heart against humanity and causes Mewtwo to exact destructive retribution against Giovanni's base before abandoning Giovanni and flying off to the ruins of the lab where he was created. Mewtwo adopts a radical, revolutionary belief that the humans and Pokémon born of this world are morally and spiritually corrupt, so it is therefore his mission to purge the planet of humans and the Pokémon they train and repopulate the planet with cloned versions of all Pokémon. With this goal, Mewtwo rebuilds the lab and enacts an elaborate plot to create a clone army for himself.

New Island, Mewtwo's base of operations and the setting for Pokémon: The First Movie.

Ash Ketchum, his friends Misty and Brock, and his main Pokémon Pikachu have been traveling on their Pokémon Journey as depicted in the anime cartoon for a large while. They soon receive an invitation to travel to the mysterious offshore locale called "New Island" to encounter and wage a traditional Pokémon battle against someone advertised as the "World’s Greatest Pokémon Master". A storm appears to disable the ferry service to the island, but Ash finds the resolve to make it to the island by the abilities of his Pokémon, making him part of a small group of highly skilled trainers awaiting the appearance of the Master (the other trainers were Corey, Fergus and Neesha). Suddenly, the Master appears, and it is none other than Mewtwo, who tells the trainers that humans are weak and cruel, and the world will fall into ruin because it is controlled by them. He also says that Pokémon are no better off, since they choose to associate with humans. Mewtwo wastes no time in explaining his agenda about proving to the world that he is in fact a living being with value, and after a series of confrontational standoffs between Mewtwo and the trainers, Mewtwo has all the trainers' Pokémon captured and cloned, forming his own clone army. Ash prepares to confront Mewtwo outright by rounding up all the original Pokémon and preparing to pit them as a force against Mewtwo's clone army in a battle for the meaning of their lives, where the winners will be the "real" Pokémon, not the worthless clones, since Mewtwo thinks that clones have no value.

Mewtwo departs with Mew and his band of clones to a new land in search of a place to live in solitude.

When Mew itself appears completely by coincidence, Mewtwo seizes the opportunity and wages a psychic aerial battle with Mew as the natural Pokémon and clone Pokémon wage a small war below, as an attempt to fight for the meaning of their lives. Meowth talks with his clone about philosophy and how tasteful it is to be talking about the moon at a time like this. The clashes herein are brutal and tire all the Pokémon out, revealing to Ash and his friends that Mewtwo and all the clones are living beings with value yet can't accept the facts. Eventually, as Mewtwo and Mew's conflict climaxes, Ash throws himself in the crossfire and is killed by the combined attacks; his body is turned into stone. Pikachu rushes to Ash's side and attempts to thundershock his friend back to life; when this proves unsuccessful, Pikachu is overcome with grief and bursts into tears. Mewtwo is taken aback by this selfless display, and all the other Pokémon grieve for the unnecessary loss of life. Their tears then forge an unexplainable miracle where Ash is revived. Mewtwo stands down, having realized that it does not matter who is more powerful and that both the clones and the originals have value. Mewtwo thus erases the minds of all involved in the event and returns them to the mainland, unaware of the drama that has just transpired. Mewtwo then destroys his lab complex and travels west with his band of clones in search of a place where they can live in peace.

However, though Mewtwo erased everyone's memories of him at New Island, he is still being targeted by Giovanni, who has been making another plan to capture and bend Mewtwo to his will. This chapter of the story plays out in the sequel Mewtwo Returns.

Pikachu’s Vacation

Pikachu’s Vacation is a 21-minute short movie that is shown before Mewtwo Strikes Back in both the theatrical and the DVD version of the main movie. It is the first of the "Pikachu shorts" in what would be a traditional process of hosting a 20+ minute mini-movie before the main Pokémon feature that would last up until the 6th movie. Pikachu’s Vacation, like the five Pikachu shorts that would follow, focuses primarily on an action-packed affair involving solely the Pokémon seen from the anime as they take part in a scenario that eventually illustrates a moral.

In Pokémon fan communities, Pikachu’s Vacation was noted for introducing the never-before-seen Pokémon character Snubbull, as well as the first primary anime appearance of the already popular Marill. This became a tradition for all Pikachu shorts, as they were used to introduce new Pokémon from the upcoming “generations” of Pokémon games, cards, and anime material. (See here for more information about generations in the Pokémon context.)

When Ash and his friends stumble upon a Pokémon-only vacation resort, they decide to let their Pokémon have a day of fun and relaxation and let all their Pokémon out as the trainers go off on their own. Pikachu and the Pokémon go off into the resort and immediately contend with an unhappy Togepi, which they succeed in doing. Soon, a group of border-ruffian Pokémon comprised of a Raichu, Cubone, Snubbull, and Marill come along and immediately cause trouble for Pikachu’s group. The ensuing standoff soon becomes a series of competitions such as a swimming race. Their increasingly passionate rivalry soon comes to a standstill when Pikachu’s companion Charizard finds its head stuck in a tight storage receptacle. Putting aside their squabble, Pikachu and Raichu’s groups join together to release Charizard, and they soon find themselves as friends for the rest of the day. At the end of the day, Pikachu and his fellow Pokémon leave the resort with fond memories and rejoin their trainers.

From Wikipedia